Find the electric field E⃗ (r⃗ )E→(r→)E_vec(r_vec) inside the sphere (for rrr< aaa) in terms of the position vector r⃗ r→r_vec. Express your answer in terms of r⃗ r→r_vec, rhorhorho (Greek letter rho), and ϵ0ϵ0epsilon_0.

Solution :

Using the Gauss law, the electric field intensity of a sphere is given by :

Now the enclosed charge inside the sphere (r<a) is

Hence, the electric field intensity becomes as follows :

Thus, the electric field inside the sphere is given by :

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